For questions related to Bell basis - i.e. converting a state to the Bell basis, working with such states and measuring in the basis.

Bell basis is composed of so-called Bell states:

  • $\frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$
  • $\frac{1}{\sqrt{2}}(|00\rangle - |11\rangle)$
  • $\frac{1}{\sqrt{2}}(|01\rangle + |10\rangle)$
  • $\frac{1}{\sqrt{2}}(|01\rangle - |10\rangle)$

This means that it described two qubit states. Or in other words, any two qubit state can be expressed as a linear combination of Bell states above.

A state can be transformed to the Bell basis by operation $\mathrm{CNOT}(H \otimes I)$. An inverse operation, i.e. $(H \otimes I)\mathrm{CNOT}$, is used for a measuring in the Bell basis